First, we used KYNSED to compute the disc flux as a function of radius and then the model half-right radius, \(R_{\rm 1/2,mod}\) , when the disc is not illuminated by the X-ray sourceAll half-radius model calculations in this paper are done for \(\lambda =2500\)  Å, so that we compare the model with the data listed in Table REF . Hence, \(R_{\rm 1/2,mod}\)  refer to the model half-radius measured at 2500 Å.. When X-ray illumination is turned off, KYNSED calculates the SED of a plane parallel, Keplerian, geometrically-thin and optically-thick accretion disc around a BH of mass \(M_{\rm BH}\)   and spin \(a^\ast \)\(^(\)\(a^\ast \)\(=Jc/G\)\(M_{\rm BH}\)\(^2\) , where \(J\)  is the angular momentum of the BH. The spin parameter is smaller or equal to 1 [1]}\(^)\) , with an accretion rate of \(\dot{m}_{\rm Edd}\) . Figure REF  shows the flux radial profile in the case of an AGN with \(M_{\rm BH}\) =\(10^8\) M\(_\odot \) , \(\dot{m}_{\rm Edd}\) =0.2, \(a^\ast \) =0 and 1 (left and right panels, respectively). The inclination angle, \(\theta \) , is set to 40. The red lines show the flux radial profile when the disc temperature is estimated ignoring the relativistic factors
(which is usually the case). The dotted blue lines show the flux profile when the temperature is properly computed, following the NT prescription. The radial profile is systematically smaller in the latter case, although the difference is not significant, except at radii smaller than \(\sim 20\)  \(R_{\rm g}\)   when \(a^\ast \) =0 (left panel in Fig. REF ).
